The broad, long-term objective of this research project is to develop new statistical methodology for analyzing multivariate or correlated failure time data from cardiovascular disease research and other biomedical studies. Multivariate failure time data arise naturally in biomedical studies. For example, in family studies, the ages of disease occurrence are recorded for members of families;in epidemiological cohort studies, individual study subjects are followed for the occurrence of different events;or, in clinical trials, patients are followed for repeated recurrent events. A common feature of the data in these examples is that the failure times could be correlated. Valid statistical methods need to account for this correlation. There are 5 specific aims in this competing renewal application. The first aim concerns statistical inferences for multivariate failure time data from case-cohort studies. Marginal hazards model will be considered and an estimating equation approach will be developed for parameter estimation. The second aim studies a class of semi-parametric additive risk model with mixed effects for multivariate failure time data. An estimating equations approach and a maximum likelihood approach are proposed for estimation. The third aim considers time-varying coefficient rate models for recurrent event data. Regression splines and penalized regression splines will be considered to estimate the time-varying coefficient. The fourth aim concerns frailty models with flexible frailty distribution for multivariate failure time data. Estimation will be based on the sieve likelihood estimation procedure. The fifth aim investigates inference procedures for marginal hazards models with multivariate failure time data from case-control studies. Parameter estimation will be conducted through a weighted estimating equation approach. The strength and weakness of each proposed method will be critically examined via theoretical investigations and simulation studies. Related software will be developed. Data sets from epidemiologic studies on cardiovascular disease and other biomedical studies will be analyzed using the proposed methods. This research will provide valuable new tools to cardiovascular disease researchers and other biomedical researchers. It will help the researchers to better understand the risk factors associated with cardiovascular diseases.